Instructor’s Solutions Manual
for
Numerical Analysis
10th EDITION
N
U
Richard L. Burden
Youngstown State University
R
J. Douglas Faires
Youngstown State University
SE
D
O
C
Prepared by
S
Richard L. Burden
Youngstown State University
J. Douglas Faires
Youngstown State University
,Table of Contents
Preface vii
N
Mathematical Preliminaries 1
Exercise Set 1.1 ....................................................................................................................................... 1
Exercise Set 1.2 ....................................................................................................................................... 6
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Exercise Set 1.3 ..................................................................................................................................... 12
Solutions of Equations of One Variable 19
Exercise Set 2.1 ..................................................................................................................................... 19
R
Exercise Set 2.2 ..................................................................................................................................... 22
Exercise Set 2.3 ..................................................................................................................................... 26
Exercise Set 2.4 ..................................................................................................................................... 31
SE
Exercise Set 2.5 ..................................................................................................................................... 34
Exercise Set 2.6 ..................................................................................................................................... 36
Interpolation and Polynomial Approximation 41
Exercise Set 3.1 ..................................................................................................................................... 41
Exercise Set 3.2 ..................................................................................................................................... 47
Exercise Set 3.3 ..................................................................................................................................... 49
D
Exercise Set 3.4 ..................................................................................................................................... 52
Exercise Set 3.5 ..................................................................................................................................... 56
Exercise Set 3.6 ..................................................................................................................................... 68
O
Numerical Differentiation and Integration 71
Exercise Set 4.1 ..................................................................................................................................... 71
Exercise Set 4.2 ..................................................................................................................................... 78
C
Exercise Set 4.3 ..................................................................................................................................... 82
Exercise Set 4.4 ..................................................................................................................................... 87
Exercise Set 4.5 ..................................................................................................................................... 91
Exercise Set 4.6 ..................................................................................................................................... 94
S
Exercise Set 4.7 ..................................................................................................................................... 96
Exercise Set 4.8 ..................................................................................................................................... 99
Exercise Set 4.9 ................................................................................................................................... 101
iii
Initial-Value Problems for Ordinary Differential Equations 105
Exercise Set 5.1 ................................................................................................................................... 105
, Exercise Set 5.2 ................................................................................................................................... 108
Exercise Set 5.3 ................................................................................................................................... 113
Exercise Set 5.4 ................................................................................................................................... 119
Exercise Set 5.5 ................................................................................................................................... 129
Exercise Set 5.6 ................................................................................................................................... 133
Exercise Set 5.7 ................................................................................................................................... 144
Exercise Set 5.8 ................................................................................................................................... 149
Exercise Set 5.9 ................................................................................................................................... 152
Exercise Set 5.10 ................................................................................................................................. 159
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Direct Methods for Solving Linear Systems 169
Exercise Set 6.1 ................................................................................................................................... 169
Exercise Set 6.2 ................................................................................................................................... 174
Exercise Set 6.3 ................................................................................................................................... 180
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Exercise Set 6.4 ................................................................................................................................... 188
Exercise Set 6.1 ................................................................................................................................... 190
Exercise Set 6.6 ................................................................................................................................... 194
R
Iterative Techniques in Matrix Algebra 201
Exercise Set 7.1 ................................................................................................................................... 201
Exercise Set 7.2 ................................................................................................................................... 206
SE
Exercise Set 7.3 ................................................................................................................................... 209
Exercise Set 7.4 ................................................................................................................................... 215
Exercise Set 7.5 ................................................................................................................................... 219
Exercise Set 7.6 ................................................................................................................................... 221
Approximation Theory 231
D
Exercise Set 8.1 ................................................................................................................................... 231
Exercise Set 8.2 ................................................................................................................................... 232
Exercise Set 8.3 ................................................................................................................................... 236
O
Exercise Set 8.4 ................................................................................................................................... 238
Exercise Set 8.5 ................................................................................................................................... 244
Exercise Set 8.6 ................................................................................................................................... 247
C
Approximating Eigenvalues 251
Exercise Set 9.1 ................................................................................................................................... 251
Exercise Set 9.2 ................................................................................................................................... 257
Exercise Set 9.3 ................................................................................................................................... 262
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Exercise Set 9.4 ................................................................................................................................... 266
Exercise Set 9.5 ................................................................................................................................... 267
Exercise Set 9.6 ................................................................................................................................... 273
Numerical Solutions of Nonlinear Systems of Equations 281
Exercise Set 10.1 ................................................................................................................................. 281
Exercise Set 10.2 ................................................................................................................................. 284
Exercise Set 10.3 ................................................................................................................................. 287
, Exercise Set 10.4 ................................................................................................................................. 290
Exercise Set 10.5 ................................................................................................................................. 291
Boundary-Value Problems for Ordinary Differential Equations 295
Exercise Set 11.1 ................................................................................................................................. 295
Exercise Set 11.2 ................................................................................................................................. 299
Exercise Set 11.3 ................................................................................................................................. 303
Exercise Set 11.4 ................................................................................................................................. 308
Exercise Set 11.5 ................................................................................................................................. 313
Numerical Solutions to Partial Differential Equations 319
Exercise Set 12.1 ................................................................................................................................. 319
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Exercise Set 12.2 ................................................................................................................................. 323
Exercise Set 12.3 ................................................................................................................................. 333
Exercise Set 12.4 ................................................................................................................................. 336
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for
Numerical Analysis
10th EDITION
N
U
Richard L. Burden
Youngstown State University
R
J. Douglas Faires
Youngstown State University
SE
D
O
C
Prepared by
S
Richard L. Burden
Youngstown State University
J. Douglas Faires
Youngstown State University
,Table of Contents
Preface vii
N
Mathematical Preliminaries 1
Exercise Set 1.1 ....................................................................................................................................... 1
Exercise Set 1.2 ....................................................................................................................................... 6
U
Exercise Set 1.3 ..................................................................................................................................... 12
Solutions of Equations of One Variable 19
Exercise Set 2.1 ..................................................................................................................................... 19
R
Exercise Set 2.2 ..................................................................................................................................... 22
Exercise Set 2.3 ..................................................................................................................................... 26
Exercise Set 2.4 ..................................................................................................................................... 31
SE
Exercise Set 2.5 ..................................................................................................................................... 34
Exercise Set 2.6 ..................................................................................................................................... 36
Interpolation and Polynomial Approximation 41
Exercise Set 3.1 ..................................................................................................................................... 41
Exercise Set 3.2 ..................................................................................................................................... 47
Exercise Set 3.3 ..................................................................................................................................... 49
D
Exercise Set 3.4 ..................................................................................................................................... 52
Exercise Set 3.5 ..................................................................................................................................... 56
Exercise Set 3.6 ..................................................................................................................................... 68
O
Numerical Differentiation and Integration 71
Exercise Set 4.1 ..................................................................................................................................... 71
Exercise Set 4.2 ..................................................................................................................................... 78
C
Exercise Set 4.3 ..................................................................................................................................... 82
Exercise Set 4.4 ..................................................................................................................................... 87
Exercise Set 4.5 ..................................................................................................................................... 91
Exercise Set 4.6 ..................................................................................................................................... 94
S
Exercise Set 4.7 ..................................................................................................................................... 96
Exercise Set 4.8 ..................................................................................................................................... 99
Exercise Set 4.9 ................................................................................................................................... 101
iii
Initial-Value Problems for Ordinary Differential Equations 105
Exercise Set 5.1 ................................................................................................................................... 105
, Exercise Set 5.2 ................................................................................................................................... 108
Exercise Set 5.3 ................................................................................................................................... 113
Exercise Set 5.4 ................................................................................................................................... 119
Exercise Set 5.5 ................................................................................................................................... 129
Exercise Set 5.6 ................................................................................................................................... 133
Exercise Set 5.7 ................................................................................................................................... 144
Exercise Set 5.8 ................................................................................................................................... 149
Exercise Set 5.9 ................................................................................................................................... 152
Exercise Set 5.10 ................................................................................................................................. 159
N
Direct Methods for Solving Linear Systems 169
Exercise Set 6.1 ................................................................................................................................... 169
Exercise Set 6.2 ................................................................................................................................... 174
Exercise Set 6.3 ................................................................................................................................... 180
U
Exercise Set 6.4 ................................................................................................................................... 188
Exercise Set 6.1 ................................................................................................................................... 190
Exercise Set 6.6 ................................................................................................................................... 194
R
Iterative Techniques in Matrix Algebra 201
Exercise Set 7.1 ................................................................................................................................... 201
Exercise Set 7.2 ................................................................................................................................... 206
SE
Exercise Set 7.3 ................................................................................................................................... 209
Exercise Set 7.4 ................................................................................................................................... 215
Exercise Set 7.5 ................................................................................................................................... 219
Exercise Set 7.6 ................................................................................................................................... 221
Approximation Theory 231
D
Exercise Set 8.1 ................................................................................................................................... 231
Exercise Set 8.2 ................................................................................................................................... 232
Exercise Set 8.3 ................................................................................................................................... 236
O
Exercise Set 8.4 ................................................................................................................................... 238
Exercise Set 8.5 ................................................................................................................................... 244
Exercise Set 8.6 ................................................................................................................................... 247
C
Approximating Eigenvalues 251
Exercise Set 9.1 ................................................................................................................................... 251
Exercise Set 9.2 ................................................................................................................................... 257
Exercise Set 9.3 ................................................................................................................................... 262
S
Exercise Set 9.4 ................................................................................................................................... 266
Exercise Set 9.5 ................................................................................................................................... 267
Exercise Set 9.6 ................................................................................................................................... 273
Numerical Solutions of Nonlinear Systems of Equations 281
Exercise Set 10.1 ................................................................................................................................. 281
Exercise Set 10.2 ................................................................................................................................. 284
Exercise Set 10.3 ................................................................................................................................. 287
, Exercise Set 10.4 ................................................................................................................................. 290
Exercise Set 10.5 ................................................................................................................................. 291
Boundary-Value Problems for Ordinary Differential Equations 295
Exercise Set 11.1 ................................................................................................................................. 295
Exercise Set 11.2 ................................................................................................................................. 299
Exercise Set 11.3 ................................................................................................................................. 303
Exercise Set 11.4 ................................................................................................................................. 308
Exercise Set 11.5 ................................................................................................................................. 313
Numerical Solutions to Partial Differential Equations 319
Exercise Set 12.1 ................................................................................................................................. 319
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Exercise Set 12.2 ................................................................................................................................. 323
Exercise Set 12.3 ................................................................................................................................. 333
Exercise Set 12.4 ................................................................................................................................. 336
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